Subgroups — C₁₇×#1416 #14524422

Order 2176.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₇×C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#366	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₁₇	—	2	1	no	—
5	C₁₇×Q₃₂	—	2	1	no	—
6	C₁₇×Q₃₂	C₄	1	2	yes	complemented
7	C₂×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
8	C₁₇×#107	—	2	1	no	—
9	C₁₇×C₃₂	—	2	1	no	—
10	C₂×Q₈×C₁₇	—	4	1	no	—
11	Q₁₆×C₁₇	—	2	2	no	—
12	Q₁₆×C₁₇	—	4	1	no	—
13	C₂×C₈×C₁₇	D₄	1	1	yes	characteristic
14	C₄⋊C₄×C₁₇	—	4	1	no	—
15	C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₁₇	D₄	1	1	yes	characteristic
17	Q₈×C₁₇	—	4	2	no	—
18	Q₈×C₁₇	—	8	1	no	—
19	C₂×C₄×C₁₇	—	8	1	no	—
20	C₂×C₄×C₁₇	—	8	1	no	—
21	C₂×C₄×C₁₇	D₈	1	1	yes	characteristic
22	C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₁₇	SD₁₆	1	1	yes	characteristic
24	#1416	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₁₇	D₁₆	1	1	yes	characteristic
26	C₄×C₁₇	—	8	2	no	—
27	C₄×C₁₇	—	16	1	no	—
28	C₄×C₁₇	#102	1	1	yes	characteristic
29	C₄×C₁₇	SD₃₂	1	1	yes	characteristic
30	C₂×Q₃₂	C₂×C₁₇	1	1	yes	characteristic
31	C₂×C₃₂	C₂×C₁₇	1	1	yes	characteristic
32	#366	C₂×C₁₇	1	1	yes	characteristic
33	C₂×C₁₇	#357	1	1	yes	characteristic
34	C₂×C₁₇	SD₆₄	1	1	yes	characteristic
35	C₂×C₁₇	Q₆₄	1	1	yes	characteristic
36	C₂×Q₁₆	—	2	1	no	—
37	Q₃₂	—	2	1	no	—
38	Q₃₂	C₄×C₁₇	1	2	yes	complemented
39	C₂×C₁₆	C₂²×C₁₇	1	1	yes	characteristic
40	#107	—	2	1	no	—
41	C₃₂	—	2	1	no	—
42	C₁₇	#1416	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×Q₈	—	4	1	no	—
44	Q₁₆	—	2	2	no	—
45	Q₁₆	—	4	1	no	—
46	C₂×C₈	D₄×C₁₇	1	1	yes	characteristic
47	C₄⋊C₄	—	4	1	no	—
48	C₁₆	C₂×C₄×C₁₇	1	1	yes	characteristic
49	C₁₆	D₄×C₁₇	1	1	yes	characteristic
50	Q₈	—	4	2	no	—
51	Q₈	—	8	1	no	—
52	C₂×C₄	—	8	1	no	—
53	C₂×C₄	—	8	1	no	—
54	C₂×C₄	D₈×C₁₇	1	1	yes	characteristic
55	C₈	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
56	C₈	SD₁₆×C₁₇	1	1	yes	characteristic
57	C₂²	C₁₇×D₁₆	1	1	yes	characteristic
58	C₄	—	8	2	no	—
59	C₄	—	16	1	no	—
60	C₄	C₁₇×#102	1	1	yes	characteristic
61	C₄	C₁₇×SD₃₂	1	1	yes	characteristic
62	C₂	C₁₇×#357	1	1	yes	characteristic
63	C₂	C₁₇×SD₆₄	1	1	yes	characteristic
64	C₂	C₁₇×Q₆₄	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₇	D₁₆
commutator	C₁₆	C₂×C₄×C₁₇
Frattini, cosocle	C₂×C₁₆	C₂²×C₁₇
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂×C₈×C₁₇ ◁ C₂×C₁₆×C₁₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
6. C₁₇×Q₃₂	C₄	semidirect
24. #1416	C₁₇	direct (N × H)
38. Q₃₂	C₄×C₁₇	semidirect
42. C₁₇	#1416	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₇×Q₃₂	2
C₂×C₁₇×C₃₂	2
C₁₇×#366	2
#1416	17

Subgroups — C17×#1416 #14524422

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#1416 #14524422